HARFA: INTRODUCTION HarFA is software that was compiled to perform harmonic and wavelet analysis of digitised images and calculations their fractal parameters. Harmonic analysis means 1D or 2D Fourier transform of image information. Harmonic analysis is provided by using fast Cooley - Tukey discrete Fourier transform algorithm (DFFT). This algorithm works with advance when the length of dataset is N (or N x N in 2D case), where N is an integer power of 2. Therefore the size of analysed area can be set to the 32, 64, 128, 256, 512, 1024, ... pixels. You can fill dataset by values of intensity (shades of grey), hue, red, green or blue components of colour information. Fourier transform is presented as MTF (Magnitude Transfer Function), PTF (Phase Transfer Function), Re and Im (Real and Imaginary) part of Fourier spectrum. Harmonic analysis can be performed either in 1D space or in 2D space. Results can be viewed as 1D, 2D (transformed images) and 3D (2D FFT only) graphs. 1D graph data can be stored as text files. Transformed images can be saved as bitmaps. On harmonic analysis is based a new method of calculation fractal dimension and fractal measure. Wavelet analysis means 1D or 2D Haar transform of image information. Wavelet analysis is provided by using fast algorithm calculation. This algorithm works with advance when the length of dataset is N (or N x N in 2D case), where N is an integer power of 2. Therefore the size of analysed area can be set to the 32, 64, 128, 256, 512, 1024, ... pixels. You can fill dataset by values of intensity (shades of grey), hue, red, green or blue components of colour information. Wavelet analysis can be performed either in 1D space or in 2D space. Results can be viewed as 1D, 2D (transformed images) and 3D (2D HT only) graphs. 1D graph data can be stored as text files. Transformed images can be saved as bitmaps. On wavelet analysis is based a new method of calculation fractal dimension and fractal measure. For special case (thresholded figure, area size equal to 1, 2, 4, 8, 16, 32, 64, 128, 256, …) is equivalent to the classical box-counting method. Fractal analysis means determination of fractal dimension and fractal measure of the image. Fractal dimension and fractal measure are obtained by using variation of Box Counting Method. By this technique we can examine black&white fractal structures which come into existence during process called "thresholding". Thresholding transforms coloured image object into black&white one. There are many criteria which can be changed to derive many different fractal structures from oneimage (e.g. you can alter minimal value of hue to be thresholded as black one, or you can determine that black will be all pixels which fulfil condition of their RGB channels - e.g. (87 <= R <=145) AND (63 <= G <= 146) AND (77 <= B <= 255)), and all the others pixels become white). So you can get various fractal dimensions and measures for one image. If you want to characterize image by its fractal dimension, you don't know which of them is appropriate. Therefore there is a possibility to establish fractal dimension of image in the whole range of thresholding conditions (Fractal Analysis - Range). Then you get something called "fractal spectrum", where fractal dimension is presented as a function of thresholding condition (e.g. fractal dimension as a function of masked intesity (shade of gray) value). Fractal spectra and data concerning every datapoint of fractal spectrum can be saved and loaded for future viewing as text files. Several filtration algorithms are included (sharpening, smoothing, median and Kuwahara filtering, different kinds of derivative filters). There are tools for suppression of thermal noise of CCD cam and for the elimination of image sample illumination non-uniformity (e.g. samples prepared by using optical microscope and CCD). Image information can be handled in four colour spaces - intensity (shades of gray), HSB/HSV (hue, saturation, brightness/value), HLS (hue, lightness, saturation) and RGB (red, green and blue channel). Previous Next